{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 1 相关分析——Spearman、Pearson系数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "try:\n",
    "    import pandas as pd\n",
    "    import numpy as np\n",
    "except:\n",
    "    !pip3 install pandas numpy matplotlib"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>平均气温x</th>\n",
       "      <th>降雨量y</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>3.8</td>\n",
       "      <td>77.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>4.0</td>\n",
       "      <td>51.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>5.8</td>\n",
       "      <td>60.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>8.0</td>\n",
       "      <td>54.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>11.3</td>\n",
       "      <td>55.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>14.4</td>\n",
       "      <td>56.8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>16.5</td>\n",
       "      <td>45.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>16.2</td>\n",
       "      <td>55.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>13.8</td>\n",
       "      <td>67.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>10.8</td>\n",
       "      <td>73.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>6.7</td>\n",
       "      <td>76.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>4.7</td>\n",
       "      <td>79.6</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    平均气温x  降雨量y\n",
       "0     3.8  77.7\n",
       "1     4.0  51.2\n",
       "2     5.8  60.1\n",
       "3     8.0  54.1\n",
       "4    11.3  55.4\n",
       "5    14.4  56.8\n",
       "6    16.5  45.0\n",
       "7    16.2  55.3\n",
       "8    13.8  67.5\n",
       "9    10.8  73.3\n",
       "10    6.7  76.6\n",
       "11    4.7  79.6"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Data = {\n",
    "    '平均气温x': [3.80, 4.00, 5.80, 8.00, 11.30, 14.40, 16.50, 16.20, 13.80, 10.80, 6.70, 4.70],\n",
    "    '降雨量y': [77.70, 51.20, 60.10, 54.10, 55.40, 56.80, 45.00, 55.30, 67.50, 73.30, 76.60, 79.60]\n",
    "}\n",
    "data = pd.DataFrame(Data)\n",
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>平均气温x</th>\n",
       "      <th>降雨量y</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>平均气温x</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.489495</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>降雨量y</th>\n",
       "      <td>-0.489495</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          平均气温x      降雨量y\n",
       "平均气温x  1.000000 -0.489495\n",
       "降雨量y  -0.489495  1.000000"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Pearson相关系数\n",
    "data.corr('pearson')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__Spearman相关系数看下面 2 pandas--read_excel最后。__  \n",
    "前面的部分是Python打开Excel常用的操作"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 2 pandas——read_excel\n",
    "\n",
    "```Python3\n",
    "pandas.read_excel(io, sheet_name=0, header=0, names=None, index_col=None, usecols=None, squeeze=False, dtype=None, engine=None, converters=None, true_values=None, false_values=None, skiprows=None, nrows=None, na_values=None, keep_default_na=True, verbose=False, parse_dates=False, date_parser=None, thousands=None, comment=None, skipfooter=0, convert_float=True, mangle_dupe_cols=True, **kwds)\n",
    "```  \n",
    "用途：Read an Excel file into a pandas DataFrame  \n",
    "支持格式：xls、xlsx、xlsm、xlsb和odf，可以是来自本地，也可以来自网络UR。\n",
    "支持读入单个或多个工作表。   \n",
    "  \n",
    "API参考：https://pandas.pydata.org/docs/reference/api/pandas.read_excel.html#pandas.read_excel\n",
    "\n",
    "## 2.1 数据准备  \n",
    "    定位到工作表\n",
    "\n",
    "__内容：__  \n",
    "1. 路径io：接受任何的字符串路径，不论是本地的file还是其他的ftp、http、s3等等。\n",
    "2. 工作表sheet_name：接受 str、int、list，or None, defult 0\n",
    "    1. 字符串对应工作表名称；\n",
    "    2. 整型对应工作表索引；\n",
    "    3. 包含字符串或者整型的列表对应多个工作表；\n",
    "    4. None 表示解析所有工作表；\n",
    " \n",
    "    \n",
    " 注：如果使用解析多个工作表，将以字典的形式输出"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\n",
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       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>省市</th>\n",
       "      <th>GDP(x)(亿元)</th>\n",
       "      <th>GDP位次R1</th>\n",
       "      <th>总人口(Y)(万人)</th>\n",
       "      <th>总人口位次R2</th>\n",
       "      <th>位次差的平方</th>\n",
       "      <th>Unnamed: 6</th>\n",
       "      <th>Unnamed: 7</th>\n",
       "      <th>Unnamed: 8</th>\n",
       "      <th>Unnamed: 9</th>\n",
       "      <th>n</th>\n",
       "      <th>显著水平α</th>\n",
       "      <th>Unnamed: 12</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>广东</td>\n",
       "      <td>13625.866128</td>\n",
       "      <td>1.0</td>\n",
       "      <td>7954.22</td>\n",
       "      <td>4.0</td>\n",
       "      <td>9</td>\n",
       "      <td>NaN</td>\n",
       "      <td>秩相关系数</td>\n",
       "      <td>0.784677</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.050</td>\n",
       "      <td>0.010</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>江苏</td>\n",
       "      <td>12460.830000</td>\n",
       "      <td>2.0</td>\n",
       "      <td>7405.82</td>\n",
       "      <td>5.0</td>\n",
       "      <td>9</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>4.0</td>\n",
       "      <td>1.000</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>山东</td>\n",
       "      <td>12435.930000</td>\n",
       "      <td>3.0</td>\n",
       "      <td>9125.00</td>\n",
       "      <td>2.0</td>\n",
       "      <td>1</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>5.0</td>\n",
       "      <td>0.900</td>\n",
       "      <td>1.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>浙江</td>\n",
       "      <td>9395.000000</td>\n",
       "      <td>4.0</td>\n",
       "      <td>4679.55</td>\n",
       "      <td>11.0</td>\n",
       "      <td>49</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>6.0</td>\n",
       "      <td>0.829</td>\n",
       "      <td>0.943</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>河北</td>\n",
       "      <td>7098.560000</td>\n",
       "      <td>5.0</td>\n",
       "      <td>6769.44</td>\n",
       "      <td>6.0</td>\n",
       "      <td>1</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>7.0</td>\n",
       "      <td>0.714</td>\n",
       "      <td>0.893</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>河南</td>\n",
       "      <td>7048.590000</td>\n",
       "      <td>6.0</td>\n",
       "      <td>9667.00</td>\n",
       "      <td>1.0</td>\n",
       "      <td>25</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>8.0</td>\n",
       "      <td>0.643</td>\n",
       "      <td>0.833</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>上海</td>\n",
       "      <td>6250.810000</td>\n",
       "      <td>7.0</td>\n",
       "      <td>1711.00</td>\n",
       "      <td>25.0</td>\n",
       "      <td>324</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>9.0</td>\n",
       "      <td>0.600</td>\n",
       "      <td>0.783</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>辽宁</td>\n",
       "      <td>6002.540000</td>\n",
       "      <td>8.0</td>\n",
       "      <td>4210.00</td>\n",
       "      <td>14.0</td>\n",
       "      <td>36</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>10.0</td>\n",
       "      <td>0.564</td>\n",
       "      <td>0.746</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>四川</td>\n",
       "      <td>5456.320000</td>\n",
       "      <td>9.0</td>\n",
       "      <td>8700.40</td>\n",
       "      <td>3.0</td>\n",
       "      <td>36</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>12.0</td>\n",
       "      <td>0.456</td>\n",
       "      <td>0.712</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>湖北</td>\n",
       "      <td>5401.710000</td>\n",
       "      <td>10.0</td>\n",
       "      <td>6001.70</td>\n",
       "      <td>9.0</td>\n",
       "      <td>1</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>14.0</td>\n",
       "      <td>0.456</td>\n",
       "      <td>0.645</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>福建</td>\n",
       "      <td>5232.170000</td>\n",
       "      <td>11.0</td>\n",
       "      <td>3488.00</td>\n",
       "      <td>18.0</td>\n",
       "      <td>49</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>16.0</td>\n",
       "      <td>0.425</td>\n",
       "      <td>0.601</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>湖南</td>\n",
       "      <td>4638.730000</td>\n",
       "      <td>12.0</td>\n",
       "      <td>6662.80</td>\n",
       "      <td>7.0</td>\n",
       "      <td>25</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>18.0</td>\n",
       "      <td>0.399</td>\n",
       "      <td>0.564</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>黑龙江</td>\n",
       "      <td>4430.000000</td>\n",
       "      <td>13.0</td>\n",
       "      <td>3815.00</td>\n",
       "      <td>16.0</td>\n",
       "      <td>9</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>20.0</td>\n",
       "      <td>0.377</td>\n",
       "      <td>0.534</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>安徽</td>\n",
       "      <td>3972.380000</td>\n",
       "      <td>14.0</td>\n",
       "      <td>6410.00</td>\n",
       "      <td>8.0</td>\n",
       "      <td>36</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>22.0</td>\n",
       "      <td>0.359</td>\n",
       "      <td>0.508</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>北京</td>\n",
       "      <td>3663.100000</td>\n",
       "      <td>15.0</td>\n",
       "      <td>1456.40</td>\n",
       "      <td>26.0</td>\n",
       "      <td>121</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>24.0</td>\n",
       "      <td>0.343</td>\n",
       "      <td>0.485</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>江西</td>\n",
       "      <td>2830.460000</td>\n",
       "      <td>16.0</td>\n",
       "      <td>4254.23</td>\n",
       "      <td>13.0</td>\n",
       "      <td>9</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>26.0</td>\n",
       "      <td>0.329</td>\n",
       "      <td>0.465</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>广西</td>\n",
       "      <td>2735.130000</td>\n",
       "      <td>17.0</td>\n",
       "      <td>4857.00</td>\n",
       "      <td>10.0</td>\n",
       "      <td>49</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>28.0</td>\n",
       "      <td>0.317</td>\n",
       "      <td>0.448</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>吉林</td>\n",
       "      <td>2522.620000</td>\n",
       "      <td>18.0</td>\n",
       "      <td>2703.70</td>\n",
       "      <td>21.0</td>\n",
       "      <td>9</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>30.0</td>\n",
       "      <td>0.306</td>\n",
       "      <td>0.432</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>云南</td>\n",
       "      <td>2465.290000</td>\n",
       "      <td>19.0</td>\n",
       "      <td>4375.60</td>\n",
       "      <td>12.0</td>\n",
       "      <td>49</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>山西</td>\n",
       "      <td>2456.590000</td>\n",
       "      <td>20.0</td>\n",
       "      <td>3314.29</td>\n",
       "      <td>19.0</td>\n",
       "      <td>1</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>天津</td>\n",
       "      <td>2447.660000</td>\n",
       "      <td>21.0</td>\n",
       "      <td>1011.30</td>\n",
       "      <td>27.0</td>\n",
       "      <td>36</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>陕西</td>\n",
       "      <td>2398.580000</td>\n",
       "      <td>22.0</td>\n",
       "      <td>3689.50</td>\n",
       "      <td>17.0</td>\n",
       "      <td>25</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>重庆</td>\n",
       "      <td>2250.560000</td>\n",
       "      <td>23.0</td>\n",
       "      <td>3130.00</td>\n",
       "      <td>20.0</td>\n",
       "      <td>9</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>内蒙古</td>\n",
       "      <td>2150.414897</td>\n",
       "      <td>24.0</td>\n",
       "      <td>2379.61</td>\n",
       "      <td>23.0</td>\n",
       "      <td>1</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>新疆</td>\n",
       "      <td>1877.610000</td>\n",
       "      <td>25.0</td>\n",
       "      <td>1933.95</td>\n",
       "      <td>24.0</td>\n",
       "      <td>1</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>贵州</td>\n",
       "      <td>1356.110000</td>\n",
       "      <td>26.0</td>\n",
       "      <td>3869.66</td>\n",
       "      <td>15.0</td>\n",
       "      <td>121</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>甘肃</td>\n",
       "      <td>1304.600000</td>\n",
       "      <td>27.0</td>\n",
       "      <td>2603.34</td>\n",
       "      <td>22.0</td>\n",
       "      <td>25</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>海南</td>\n",
       "      <td>670.930000</td>\n",
       "      <td>28.0</td>\n",
       "      <td>810.52</td>\n",
       "      <td>28.0</td>\n",
       "      <td>0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>青海</td>\n",
       "      <td>390.210000</td>\n",
       "      <td>29.0</td>\n",
       "      <td>533.80</td>\n",
       "      <td>30.0</td>\n",
       "      <td>1</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>宁夏</td>\n",
       "      <td>385.340000</td>\n",
       "      <td>30.0</td>\n",
       "      <td>580.30</td>\n",
       "      <td>29.0</td>\n",
       "      <td>1</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>30</th>\n",
       "      <td>西藏</td>\n",
       "      <td>184.500000</td>\n",
       "      <td>31.0</td>\n",
       "      <td>270.17</td>\n",
       "      <td>31.0</td>\n",
       "      <td>0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>31</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1068</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     省市    GDP(x)(亿元)  GDP位次R1  总人口(Y)(万人)  总人口位次R2  位次差的平方  Unnamed: 6  \\\n",
       "0    广东  13625.866128      1.0     7954.22      4.0       9         NaN   \n",
       "1    江苏  12460.830000      2.0     7405.82      5.0       9         NaN   \n",
       "2    山东  12435.930000      3.0     9125.00      2.0       1         NaN   \n",
       "3    浙江   9395.000000      4.0     4679.55     11.0      49         NaN   \n",
       "4    河北   7098.560000      5.0     6769.44      6.0       1         NaN   \n",
       "5    河南   7048.590000      6.0     9667.00      1.0      25         NaN   \n",
       "6    上海   6250.810000      7.0     1711.00     25.0     324         NaN   \n",
       "7    辽宁   6002.540000      8.0     4210.00     14.0      36         NaN   \n",
       "8    四川   5456.320000      9.0     8700.40      3.0      36         NaN   \n",
       "9    湖北   5401.710000     10.0     6001.70      9.0       1         NaN   \n",
       "10   福建   5232.170000     11.0     3488.00     18.0      49         NaN   \n",
       "11   湖南   4638.730000     12.0     6662.80      7.0      25         NaN   \n",
       "12  黑龙江   4430.000000     13.0     3815.00     16.0       9         NaN   \n",
       "13   安徽   3972.380000     14.0     6410.00      8.0      36         NaN   \n",
       "14   北京   3663.100000     15.0     1456.40     26.0     121         NaN   \n",
       "15   江西   2830.460000     16.0     4254.23     13.0       9         NaN   \n",
       "16   广西   2735.130000     17.0     4857.00     10.0      49         NaN   \n",
       "17   吉林   2522.620000     18.0     2703.70     21.0       9         NaN   \n",
       "18   云南   2465.290000     19.0     4375.60     12.0      49         NaN   \n",
       "19   山西   2456.590000     20.0     3314.29     19.0       1         NaN   \n",
       "20   天津   2447.660000     21.0     1011.30     27.0      36         NaN   \n",
       "21   陕西   2398.580000     22.0     3689.50     17.0      25         NaN   \n",
       "22   重庆   2250.560000     23.0     3130.00     20.0       9         NaN   \n",
       "23  内蒙古   2150.414897     24.0     2379.61     23.0       1         NaN   \n",
       "24   新疆   1877.610000     25.0     1933.95     24.0       1         NaN   \n",
       "25   贵州   1356.110000     26.0     3869.66     15.0     121         NaN   \n",
       "26   甘肃   1304.600000     27.0     2603.34     22.0      25         NaN   \n",
       "27   海南    670.930000     28.0      810.52     28.0       0         NaN   \n",
       "28   青海    390.210000     29.0      533.80     30.0       1         NaN   \n",
       "29   宁夏    385.340000     30.0      580.30     29.0       1         NaN   \n",
       "30   西藏    184.500000     31.0      270.17     31.0       0         NaN   \n",
       "31  NaN           NaN      NaN         NaN      NaN    1068         NaN   \n",
       "\n",
       "   Unnamed: 7  Unnamed: 8  Unnamed: 9     n  显著水平α  Unnamed: 12  \n",
       "0       秩相关系数    0.784677         NaN   NaN  0.050        0.010  \n",
       "1         NaN         NaN         NaN   4.0  1.000          NaN  \n",
       "2         NaN         NaN         NaN   5.0  0.900        1.000  \n",
       "3         NaN         NaN         NaN   6.0  0.829        0.943  \n",
       "4         NaN         NaN         NaN   7.0  0.714        0.893  \n",
       "5         NaN         NaN         NaN   8.0  0.643        0.833  \n",
       "6         NaN         NaN         NaN   9.0  0.600        0.783  \n",
       "7         NaN         NaN         NaN  10.0  0.564        0.746  \n",
       "8         NaN         NaN         NaN  12.0  0.456        0.712  \n",
       "9         NaN         NaN         NaN  14.0  0.456        0.645  \n",
       "10        NaN         NaN         NaN  16.0  0.425        0.601  \n",
       "11        NaN         NaN         NaN  18.0  0.399        0.564  \n",
       "12        NaN         NaN         NaN  20.0  0.377        0.534  \n",
       "13        NaN         NaN         NaN  22.0  0.359        0.508  \n",
       "14        NaN         NaN         NaN  24.0  0.343        0.485  \n",
       "15        NaN         NaN         NaN  26.0  0.329        0.465  \n",
       "16        NaN         NaN         NaN  28.0  0.317        0.448  \n",
       "17        NaN         NaN         NaN  30.0  0.306        0.432  \n",
       "18        NaN         NaN         NaN   NaN    NaN          NaN  \n",
       "19        NaN         NaN         NaN   NaN    NaN          NaN  \n",
       "20        NaN         NaN         NaN   NaN    NaN          NaN  \n",
       "21        NaN         NaN         NaN   NaN    NaN          NaN  \n",
       "22        NaN         NaN         NaN   NaN    NaN          NaN  \n",
       "23        NaN         NaN         NaN   NaN    NaN          NaN  \n",
       "24        NaN         NaN         NaN   NaN    NaN          NaN  \n",
       "25        NaN         NaN         NaN   NaN    NaN          NaN  \n",
       "26        NaN         NaN         NaN   NaN    NaN          NaN  \n",
       "27        NaN         NaN         NaN   NaN    NaN          NaN  \n",
       "28        NaN         NaN         NaN   NaN    NaN          NaN  \n",
       "29        NaN         NaN         NaN   NaN    NaN          NaN  \n",
       "30        NaN         NaN         NaN   NaN    NaN          NaN  \n",
       "31        NaN         NaN         NaN   NaN    NaN          NaN  "
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# sheet_name表明需要解析那张表格，默认为0（第一张）\n",
    "data1 = pd.read_excel('/home/Ubuntu/Documents/test.xlsx', sheet_name=2)\n",
    "data1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__内容：__ \n",
    "   3. 列标签header: 默认defult 0，可以接受一个整数或者一个整数列表，整数所在的行作为列标签，整数列表则是表示多重标签。如果不需要列名，使用None。\n",
    "   4. 自定义列名names: \n",
    "      1. 基于header的基础上，接收列表，定义列名；\n",
    "      2. 不能与header=None同时使用；\n",
    "      3. names的长度必须和Excel列长度一致。\n",
    "   5. 行标签index_col: 与header类似。\n",
    "   6. 强制规定列数据类型converters，传入字典{列：类型}，dtype类似。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>4</th>\n",
       "      <th>5</th>\n",
       "      <th>6</th>\n",
       "      <th>7</th>\n",
       "      <th>8</th>\n",
       "      <th>9</th>\n",
       "      <th>10</th>\n",
       "      <th>11</th>\n",
       "      <th>12</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>省市</td>\n",
       "      <td>GDP(x)(亿元)</td>\n",
       "      <td>GDP位次R1</td>\n",
       "      <td>总人口(Y)(万人)</td>\n",
       "      <td>总人口位次R2</td>\n",
       "      <td>位次差的平方</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>n</td>\n",
       "      <td>显著水平α</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>广东</td>\n",
       "      <td>13625.9</td>\n",
       "      <td>1</td>\n",
       "      <td>7954.22</td>\n",
       "      <td>4</td>\n",
       "      <td>9</td>\n",
       "      <td>NaN</td>\n",
       "      <td>秩相关系数</td>\n",
       "      <td>0.784677</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.05</td>\n",
       "      <td>0.010</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>江苏</td>\n",
       "      <td>12460.8</td>\n",
       "      <td>2</td>\n",
       "      <td>7405.82</td>\n",
       "      <td>5</td>\n",
       "      <td>9</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>山东</td>\n",
       "      <td>12435.9</td>\n",
       "      <td>3</td>\n",
       "      <td>9125</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>5</td>\n",
       "      <td>0.9</td>\n",
       "      <td>1.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>浙江</td>\n",
       "      <td>9395</td>\n",
       "      <td>4</td>\n",
       "      <td>4679.55</td>\n",
       "      <td>11</td>\n",
       "      <td>49</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>6</td>\n",
       "      <td>0.829</td>\n",
       "      <td>0.943</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   0           1        2           3        4       5   6      7         8   \\\n",
       "0  省市  GDP(x)(亿元)  GDP位次R1  总人口(Y)(万人)  总人口位次R2  位次差的平方 NaN    NaN       NaN   \n",
       "1  广东     13625.9        1     7954.22        4       9 NaN  秩相关系数  0.784677   \n",
       "2  江苏     12460.8        2     7405.82        5       9 NaN    NaN       NaN   \n",
       "3  山东     12435.9        3        9125        2       1 NaN    NaN       NaN   \n",
       "4  浙江        9395        4     4679.55       11      49 NaN    NaN       NaN   \n",
       "\n",
       "   9    10     11     12  \n",
       "0 NaN    n  显著水平α    NaN  \n",
       "1 NaN  NaN   0.05  0.010  \n",
       "2 NaN    4      1    NaN  \n",
       "3 NaN    5    0.9  1.000  \n",
       "4 NaN    6  0.829  0.943  "
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 列标签header\n",
    "data2 = pd.read_excel('/home/Ubuntu/Documents/test.xlsx', 2, header=None)\n",
    "# 展示前5行\n",
    "data2.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
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       "      <th></th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>4</th>\n",
       "      <th>5</th>\n",
       "      <th>6</th>\n",
       "      <th>7</th>\n",
       "      <th>8</th>\n",
       "      <th>9</th>\n",
       "      <th>10</th>\n",
       "      <th>11</th>\n",
       "      <th>12</th>\n",
       "      <th>13</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>广东</td>\n",
       "      <td>13625.866128</td>\n",
       "      <td>1.0</td>\n",
       "      <td>7954.22</td>\n",
       "      <td>4.0</td>\n",
       "      <td>9</td>\n",
       "      <td>NaN</td>\n",
       "      <td>秩相关系数</td>\n",
       "      <td>0.784677</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.050</td>\n",
       "      <td>0.010</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>江苏</td>\n",
       "      <td>12460.830000</td>\n",
       "      <td>2.0</td>\n",
       "      <td>7405.82</td>\n",
       "      <td>5.0</td>\n",
       "      <td>9</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>4.0</td>\n",
       "      <td>1.000</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>山东</td>\n",
       "      <td>12435.930000</td>\n",
       "      <td>3.0</td>\n",
       "      <td>9125.00</td>\n",
       "      <td>2.0</td>\n",
       "      <td>1</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>5.0</td>\n",
       "      <td>0.900</td>\n",
       "      <td>1.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>浙江</td>\n",
       "      <td>9395.000000</td>\n",
       "      <td>4.0</td>\n",
       "      <td>4679.55</td>\n",
       "      <td>11.0</td>\n",
       "      <td>49</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>6.0</td>\n",
       "      <td>0.829</td>\n",
       "      <td>0.943</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>河北</td>\n",
       "      <td>7098.560000</td>\n",
       "      <td>5.0</td>\n",
       "      <td>6769.44</td>\n",
       "      <td>6.0</td>\n",
       "      <td>1</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>7.0</td>\n",
       "      <td>0.714</td>\n",
       "      <td>0.893</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   1             2    3        4     5   6   7      8         9   10   11  \\\n",
       "0  广东  13625.866128  1.0  7954.22   4.0   9 NaN  秩相关系数  0.784677 NaN  NaN   \n",
       "1  江苏  12460.830000  2.0  7405.82   5.0   9 NaN    NaN       NaN NaN  4.0   \n",
       "2  山东  12435.930000  3.0  9125.00   2.0   1 NaN    NaN       NaN NaN  5.0   \n",
       "3  浙江   9395.000000  4.0  4679.55  11.0  49 NaN    NaN       NaN NaN  6.0   \n",
       "4  河北   7098.560000  5.0  6769.44   6.0   1 NaN    NaN       NaN NaN  7.0   \n",
       "\n",
       "      12     13  \n",
       "0  0.050  0.010  \n",
       "1  1.000    NaN  \n",
       "2  0.900  1.000  \n",
       "3  0.829  0.943  \n",
       "4  0.714  0.893  "
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 自定义列名names\n",
    "data3 = pd.read_excel('/home/Ubuntu/Documents/test.xlsx', 2, names=[1,2,3,4,5,6,7,8,9,10,11,12,13])\n",
    "# 展示前5行\n",
    "data3.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2.2 数据筛选  \n",
    "    定位到某一区域\n",
    "### 2.2.1 解析特定列usecols\n",
    "\n",
    "可传入 str、list\n",
    "\n",
    "其中，\n",
    "1. 如果是str，表示Excel列字母和列范围的列表（如：\"A:E\" 或 \"A,C,E:F\")；\n",
    "2. 列表可以是字符串或整型，字符串表示列名称，整型表示列索引。\n",
    "\n",
    "\n",
    "注：解析特定行用nrows参数。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>GDP(x)(亿元)</th>\n",
       "      <th>总人口(Y)(万人)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>13625.866128</td>\n",
       "      <td>7954.22</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>12460.830000</td>\n",
       "      <td>7405.82</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>12435.930000</td>\n",
       "      <td>9125.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>9395.000000</td>\n",
       "      <td>4679.55</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>7098.560000</td>\n",
       "      <td>6769.44</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>7048.590000</td>\n",
       "      <td>9667.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>6250.810000</td>\n",
       "      <td>1711.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>6002.540000</td>\n",
       "      <td>4210.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>5456.320000</td>\n",
       "      <td>8700.40</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>5401.710000</td>\n",
       "      <td>6001.70</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>5232.170000</td>\n",
       "      <td>3488.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>4638.730000</td>\n",
       "      <td>6662.80</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>4430.000000</td>\n",
       "      <td>3815.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>3972.380000</td>\n",
       "      <td>6410.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>3663.100000</td>\n",
       "      <td>1456.40</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>2830.460000</td>\n",
       "      <td>4254.23</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>2735.130000</td>\n",
       "      <td>4857.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>2522.620000</td>\n",
       "      <td>2703.70</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>2465.290000</td>\n",
       "      <td>4375.60</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>2456.590000</td>\n",
       "      <td>3314.29</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>2447.660000</td>\n",
       "      <td>1011.30</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>2398.580000</td>\n",
       "      <td>3689.50</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>2250.560000</td>\n",
       "      <td>3130.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>2150.414897</td>\n",
       "      <td>2379.61</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>1877.610000</td>\n",
       "      <td>1933.95</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>1356.110000</td>\n",
       "      <td>3869.66</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>1304.600000</td>\n",
       "      <td>2603.34</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>670.930000</td>\n",
       "      <td>810.52</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>390.210000</td>\n",
       "      <td>533.80</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>385.340000</td>\n",
       "      <td>580.30</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>30</th>\n",
       "      <td>184.500000</td>\n",
       "      <td>270.17</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>31</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      GDP(x)(亿元)  总人口(Y)(万人)\n",
       "0   13625.866128     7954.22\n",
       "1   12460.830000     7405.82\n",
       "2   12435.930000     9125.00\n",
       "3    9395.000000     4679.55\n",
       "4    7098.560000     6769.44\n",
       "5    7048.590000     9667.00\n",
       "6    6250.810000     1711.00\n",
       "7    6002.540000     4210.00\n",
       "8    5456.320000     8700.40\n",
       "9    5401.710000     6001.70\n",
       "10   5232.170000     3488.00\n",
       "11   4638.730000     6662.80\n",
       "12   4430.000000     3815.00\n",
       "13   3972.380000     6410.00\n",
       "14   3663.100000     1456.40\n",
       "15   2830.460000     4254.23\n",
       "16   2735.130000     4857.00\n",
       "17   2522.620000     2703.70\n",
       "18   2465.290000     4375.60\n",
       "19   2456.590000     3314.29\n",
       "20   2447.660000     1011.30\n",
       "21   2398.580000     3689.50\n",
       "22   2250.560000     3130.00\n",
       "23   2150.414897     2379.61\n",
       "24   1877.610000     1933.95\n",
       "25   1356.110000     3869.66\n",
       "26   1304.600000     2603.34\n",
       "27    670.930000      810.52\n",
       "28    390.210000      533.80\n",
       "29    385.340000      580.30\n",
       "30    184.500000      270.17\n",
       "31           NaN         NaN"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data4 = pd.read_excel('/home/Ubuntu/Documents/test.xlsx', sheet_name=2, usecols=['GDP(x)(亿元)', '总人口(Y)(万人)'])\n",
    "data4 "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.2.2 跳过开头结尾的的行\n",
    "  以哪行开始、以哪行结束  \n",
    "\n",
    "skiprows：list-like  \n",
    "  + Rows to skip at the beginning (0-indexed).  \n",
    "      \n",
    "skipfooterint, default 0  \n",
    "  + Rows at the end to skip (0-indexed)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
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       "\n",
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       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>GDP(x)(亿元)</th>\n",
       "      <th>总人口(Y)(万人)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>13625.866128</td>\n",
       "      <td>7954.22</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>12460.830000</td>\n",
       "      <td>7405.82</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>12435.930000</td>\n",
       "      <td>9125.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>9395.000000</td>\n",
       "      <td>4679.55</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>7098.560000</td>\n",
       "      <td>6769.44</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>7048.590000</td>\n",
       "      <td>9667.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>6250.810000</td>\n",
       "      <td>1711.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>6002.540000</td>\n",
       "      <td>4210.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>5456.320000</td>\n",
       "      <td>8700.40</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>5401.710000</td>\n",
       "      <td>6001.70</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>5232.170000</td>\n",
       "      <td>3488.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>4638.730000</td>\n",
       "      <td>6662.80</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>4430.000000</td>\n",
       "      <td>3815.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>3972.380000</td>\n",
       "      <td>6410.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>3663.100000</td>\n",
       "      <td>1456.40</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>2830.460000</td>\n",
       "      <td>4254.23</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>2735.130000</td>\n",
       "      <td>4857.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>2522.620000</td>\n",
       "      <td>2703.70</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>2465.290000</td>\n",
       "      <td>4375.60</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>2456.590000</td>\n",
       "      <td>3314.29</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>2447.660000</td>\n",
       "      <td>1011.30</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>2398.580000</td>\n",
       "      <td>3689.50</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>2250.560000</td>\n",
       "      <td>3130.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>2150.414897</td>\n",
       "      <td>2379.61</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>1877.610000</td>\n",
       "      <td>1933.95</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>1356.110000</td>\n",
       "      <td>3869.66</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>1304.600000</td>\n",
       "      <td>2603.34</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>670.930000</td>\n",
       "      <td>810.52</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>390.210000</td>\n",
       "      <td>533.80</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>385.340000</td>\n",
       "      <td>580.30</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>30</th>\n",
       "      <td>184.500000</td>\n",
       "      <td>270.17</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      GDP(x)(亿元)  总人口(Y)(万人)\n",
       "0   13625.866128     7954.22\n",
       "1   12460.830000     7405.82\n",
       "2   12435.930000     9125.00\n",
       "3    9395.000000     4679.55\n",
       "4    7098.560000     6769.44\n",
       "5    7048.590000     9667.00\n",
       "6    6250.810000     1711.00\n",
       "7    6002.540000     4210.00\n",
       "8    5456.320000     8700.40\n",
       "9    5401.710000     6001.70\n",
       "10   5232.170000     3488.00\n",
       "11   4638.730000     6662.80\n",
       "12   4430.000000     3815.00\n",
       "13   3972.380000     6410.00\n",
       "14   3663.100000     1456.40\n",
       "15   2830.460000     4254.23\n",
       "16   2735.130000     4857.00\n",
       "17   2522.620000     2703.70\n",
       "18   2465.290000     4375.60\n",
       "19   2456.590000     3314.29\n",
       "20   2447.660000     1011.30\n",
       "21   2398.580000     3689.50\n",
       "22   2250.560000     3130.00\n",
       "23   2150.414897     2379.61\n",
       "24   1877.610000     1933.95\n",
       "25   1356.110000     3869.66\n",
       "26   1304.600000     2603.34\n",
       "27    670.930000      810.52\n",
       "28    390.210000      533.80\n",
       "29    385.340000      580.30\n",
       "30    184.500000      270.17"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data5 = pd.read_excel('/home/Ubuntu/Documents/test.xlsx', sheet_name=2, usecols=['GDP(x)(亿元)', '总人口(Y)(万人)'], skipfooter=1)\n",
    "data5 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>GDP(x)(亿元)</th>\n",
       "      <th>总人口(Y)(万人)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>GDP(x)(亿元)</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.784677</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>总人口(Y)(万人)</th>\n",
       "      <td>0.784677</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            GDP(x)(亿元)  总人口(Y)(万人)\n",
       "GDP(x)(亿元)    1.000000    0.784677\n",
       "总人口(Y)(万人)    0.784677    1.000000"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 计算 spearman 相关系数\n",
    "data5.corr('spearman') "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 3 回归分析   \n",
    "## 3.1 一元线性回归  \n",
    "__建立模型：__  \n",
    "   1. __选取__ 一元线性回归模型的 __变量__ ；\n",
    "   2. 绘制计算表和拟合散点图;\n",
    "   3. 计算变量间的回归系数及其相关的显著性；\n",
    "   4. 回归分析结果的应用。\n",
    "\n",
    "__模型的检验__:  \n",
    "   1. 经济意义检验：就是根据模型中各个参数的经济含义，分析各参数的值是否与分析对象的经济含义相符；\n",
    "   2. 回归标准差检验；\n",
    "   3. 拟合优度检验；\n",
    "   4. 回归系数的显著性检验。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy import stats\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "%config InlineBackend.figure_format = 'svg'  # 转化成矢量图，提高清晰度"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "    }\n",
       "\n",
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       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>台站</th>\n",
       "      <th>经度x/度</th>\n",
       "      <th>纬度y/度</th>\n",
       "      <th>海拔a/m</th>\n",
       "      <th>年降水量p/mm</th>\n",
       "      <th>年蒸发量v/mm</th>\n",
       "      <th>Unnamed: 6</th>\n",
       "      <th>Unnamed: 7</th>\n",
       "      <th>相关系数</th>\n",
       "      <th>Unnamed: 9</th>\n",
       "      <th>Unnamed: 10</th>\n",
       "      <th>Unnamed: 11</th>\n",
       "      <th>Unnamed: 12</th>\n",
       "      <th>Unnamed: 13</th>\n",
       "      <th>Unnamed: 14</th>\n",
       "      <th>Unnamed: 15</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>安西</td>\n",
       "      <td>95.92</td>\n",
       "      <td>40.50</td>\n",
       "      <td>1170.8</td>\n",
       "      <td>48.25</td>\n",
       "      <td>2835.57</td>\n",
       "      <td>NaN</td>\n",
       "      <td>py</td>\n",
       "      <td>-0.903529</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>白银</td>\n",
       "      <td>104.53</td>\n",
       "      <td>36.60</td>\n",
       "      <td>1707.2</td>\n",
       "      <td>193.72</td>\n",
       "      <td>1947.97</td>\n",
       "      <td>NaN</td>\n",
       "      <td>vy</td>\n",
       "      <td>0.880732</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>定西</td>\n",
       "      <td>104.63</td>\n",
       "      <td>35.53</td>\n",
       "      <td>1908.8</td>\n",
       "      <td>413.94</td>\n",
       "      <td>1538.10</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>古浪</td>\n",
       "      <td>102.90</td>\n",
       "      <td>37.48</td>\n",
       "      <td>2072.4</td>\n",
       "      <td>358.60</td>\n",
       "      <td>1756.79</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>和政</td>\n",
       "      <td>103.35</td>\n",
       "      <td>35.43</td>\n",
       "      <td>2136.4</td>\n",
       "      <td>615.04</td>\n",
       "      <td>1317.64</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>57</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>58</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>Coefficients</td>\n",
       "      <td>标准误差</td>\n",
       "      <td>t Stat</td>\n",
       "      <td>P-value</td>\n",
       "      <td>Lower 95%</td>\n",
       "      <td>Upper 95%</td>\n",
       "      <td>下限 95.0%</td>\n",
       "      <td>上限 95.0%</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>59</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>Intercept</td>\n",
       "      <td>3295.13</td>\n",
       "      <td>205.455</td>\n",
       "      <td>16.0382</td>\n",
       "      <td>2.37198e-21</td>\n",
       "      <td>2882.46</td>\n",
       "      <td>3707.8</td>\n",
       "      <td>2882.46</td>\n",
       "      <td>3707.8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>60</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>X Variable 1</td>\n",
       "      <td>-81.1737</td>\n",
       "      <td>5.38605</td>\n",
       "      <td>-15.0711</td>\n",
       "      <td>3.15159e-20</td>\n",
       "      <td>-91.9919</td>\n",
       "      <td>-70.3555</td>\n",
       "      <td>-91.9919</td>\n",
       "      <td>-70.3555</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>61</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>X Variable 2</td>\n",
       "      <td>0.036214</td>\n",
       "      <td>0.0208951</td>\n",
       "      <td>1.73313</td>\n",
       "      <td>0.0892358</td>\n",
       "      <td>-0.00575503</td>\n",
       "      <td>0.078183</td>\n",
       "      <td>-0.00575503</td>\n",
       "      <td>0.078183</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>62 rows × 16 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "     台站   经度x/度  纬度y/度   海拔a/m  年降水量p/mm  年蒸发量v/mm  Unnamed: 6    Unnamed: 7  \\\n",
       "0    安西   95.92  40.50  1170.8     48.25   2835.57         NaN            py   \n",
       "1    白银  104.53  36.60  1707.2    193.72   1947.97         NaN            vy   \n",
       "2    定西  104.63  35.53  1908.8    413.94   1538.10         NaN           NaN   \n",
       "3    古浪  102.90  37.48  2072.4    358.60   1756.79         NaN           NaN   \n",
       "4    和政  103.35  35.43  2136.4    615.04   1317.64         NaN           NaN   \n",
       "..  ...     ...    ...     ...       ...       ...         ...           ...   \n",
       "57  NaN     NaN    NaN     NaN       NaN       NaN         NaN           NaN   \n",
       "58  NaN     NaN    NaN     NaN       NaN       NaN         NaN           NaN   \n",
       "59  NaN     NaN    NaN     NaN       NaN       NaN         NaN     Intercept   \n",
       "60  NaN     NaN    NaN     NaN       NaN       NaN         NaN  X Variable 1   \n",
       "61  NaN     NaN    NaN     NaN       NaN       NaN         NaN  X Variable 2   \n",
       "\n",
       "            相关系数 Unnamed: 9 Unnamed: 10  Unnamed: 11 Unnamed: 12 Unnamed: 13  \\\n",
       "0      -0.903529        NaN         NaN          NaN         NaN         NaN   \n",
       "1       0.880732        NaN         NaN          NaN         NaN         NaN   \n",
       "2            NaN        NaN         NaN          NaN         NaN         NaN   \n",
       "3            NaN        NaN         NaN          NaN         NaN         NaN   \n",
       "4            NaN        NaN         NaN          NaN         NaN         NaN   \n",
       "..           ...        ...         ...          ...         ...         ...   \n",
       "57           NaN        NaN         NaN          NaN         NaN         NaN   \n",
       "58  Coefficients       标准误差      t Stat      P-value   Lower 95%   Upper 95%   \n",
       "59       3295.13    205.455     16.0382  2.37198e-21     2882.46      3707.8   \n",
       "60      -81.1737    5.38605    -15.0711  3.15159e-20    -91.9919    -70.3555   \n",
       "61      0.036214  0.0208951     1.73313    0.0892358 -0.00575503    0.078183   \n",
       "\n",
       "   Unnamed: 14 Unnamed: 15  \n",
       "0          NaN         NaN  \n",
       "1          NaN         NaN  \n",
       "2          NaN         NaN  \n",
       "3          NaN         NaN  \n",
       "4          NaN         NaN  \n",
       "..         ...         ...  \n",
       "57         NaN         NaN  \n",
       "58    下限 95.0%    上限 95.0%  \n",
       "59     2882.46      3707.8  \n",
       "60    -91.9919    -70.3555  \n",
       "61 -0.00575503    0.078183  \n",
       "\n",
       "[62 rows x 16 columns]"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 完整sheet在pandas中查看\n",
    "data6 = pd.read_excel('/home/Ubuntu/Documents/test.xlsx', sheet_name=1)\n",
    "data6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   纬度y/度  年降水量p/mm\n",
      "0  40.50     48.25\n",
      "1  36.60    193.72\n",
      "2  35.53    413.94\n",
      "3  37.48    358.60\n",
      "4  35.43    615.04\n",
      "    纬度y/度  年降水量p/mm\n",
      "48  34.70    515.02\n",
      "49  35.00    545.72\n",
      "50  34.21    786.75\n",
      "51  35.43    584.89\n",
      "52  36.14    574.00\n"
     ]
    }
   ],
   "source": [
    "# 数据筛选\n",
    "data7 = pd.read_excel('/home/Ubuntu/Documents/test.xlsx', sheet_name=1, usecols=['纬度y/度', '年降水量p/mm'], skipfooter=9)\n",
    "# 观察前后五行\n",
    "print(data7.head(5))\n",
    "print(data7.tail(5))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
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     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
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   "source": [
    "# 散点图观察趋势\n",
    "plt.scatter(\n",
    "    data7['纬度y/度'],\n",
    "    data7['年降水量p/mm'],\n",
    ")\n",
    "plt.xlabel('latitud')\n",
    "plt.ylabel('amount of precipitation')"
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   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 计算参数\n",
    "x = data7['纬度y/度'].values\n",
    "y = data7['年降水量p/mm'].values\n",
    "\n",
    "#############参数说明#############\n",
    "# slope：斜率                    #\n",
    "# intercept：截距                #\n",
    "# r_value：相关系数              #\n",
    "# p_value：假设检验P值           #\n",
    "# sts_err：标准误差              #\n",
    "##################################\n",
    "\n",
    "slope, intercept, r_value, p_value, std_err = stats.linregress(x,y)"
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       "<Figure size 432x288 with 1 Axes>"
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     "output_type": "display_data"
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   ],
   "source": [
    "# 曲线拟合\n",
    "plt.scatter(\n",
    "    data7['纬度y/度'],\n",
    "    data7['年降水量p/mm'],\n",
    ")\n",
    "\n",
    "predictions = slope*data7['纬度y/度'] + intercept\n",
    "plt.plot(\n",
    "    data7['纬度y/度'],\n",
    "    predictions,\n",
    "    c='black',\n",
    "    linewidth=2\n",
    ")\n",
    "plt.xlabel('纬度y/度')\n",
    "plt.ylabel('年降水量p/mm')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__显著性检验参数有：__   \n",
    "  1. 回归系数检验（t-检验）\n",
    "  2. 拟合优度R<sup>2</sup>\n",
    "  3. 模型检验(F检验）\n",
    "\n",
    "在一元线性回归分析中，三者可以转化、检验效果基本一致。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The linear model is: y = -82.188x + 3395.6\n",
      "r-squared: 0.8163651594029047\n"
     ]
    }
   ],
   "source": [
    "# 显著性检验 R²\n",
    "print(\"The linear model is: y = {:.5}x + {:.5}\".format(slope, intercept))\n",
    "print(\"r-squared:\", r_value**2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__补充：__  \n",
    "Python实现一元线性回归的8种方法：\n",
    "  1. Simple matrix inverse;\n",
    "  2. Stats.linregress;\n",
    "  3. Numpy.linalg.lstsq;\n",
    "  4. Moore-Penrose inverse;\n",
    "  5. sklearn.linear_model;\n",
    "  6. Polyfit;\n",
    "  7. Statsmodels.OLS;\n",
    "  8. Optimize.curve_fit。\n",
    "\n",
    "排名按速度快慢的顺序，其中Statsmodels.OLS()结果像R或Julia等统计语言一样丰富。所以你也可以搭配使用，你可以用sklearn。linalg_model来进行训练预测，用statsmodel.OLS来进行模型评估的。\n",
    "\n",
    "参考文章：\n",
    "https://blog.csdn.net/tMb8Z9Vdm66wH68VX1/article/details/79102425   \n",
    "原文地址：  \n",
    "https://medium.freecodecamp.org/data-science-with-python-8-ways-to-do-linear-regression-and-measure-their-speed-b5577d75f8b  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3.2 多元线性分析  \n",
    "\n",
    "多元与一元基本一致，基本过程有选取变量、建模、检验。  \n",
    "\n",
    "__Tip：__ 进行多元线性回归分析时就不能再用Stats.linregress了，它只能进行一元线性回归分析。进行多元线性回归以及非线性关系的线性化都可以用sklearn.linear_modle，[API参考](https://scikit-learn.org/stable/modules/classes.html#module-sklearn.linear_model)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   纬度y/度   海拔a/m  年降水量p/mm\n",
      "0  40.50  1170.8     48.25\n",
      "1  36.60  1707.2    193.72\n",
      "2  35.53  1908.8    413.94\n",
      "3  37.48  2072.4    358.60\n",
      "4  35.43  2136.4    615.04\n",
      "    纬度y/度   海拔a/m  年降水量p/mm\n",
      "48  34.70  2810.2    515.02\n",
      "49  35.00  2915.7    545.72\n",
      "50  34.21  3362.7    786.75\n",
      "51  35.43  1221.2    584.89\n",
      "52  36.14  1111.7    574.00\n"
     ]
    }
   ],
   "source": [
    "from sklearn import linear_model\n",
    "\n",
    "\n",
    "# 数据清洗\n",
    "data8 = pd.read_excel('/home/Ubuntu/Documents/test.xlsx', sheet_name=1, usecols=['纬度y/度', '海拔a/m', '年降水量p/mm'], skipfooter=9)\n",
    "# 清洗结果查看\n",
    "print(data8.head())\n",
    "print(data8.tail())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 选取变量\n",
    "x = data8.drop(['年降水量p/mm'], axis=1)\n",
    "y = data8.drop(['纬度y/度', '海拔a/m'], axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The linear model is: Y = 3295.1 + -81.174*维度 + 0.036214*海拔\n"
     ]
    }
   ],
   "source": [
    "# 创建线性回归对象\n",
    "regr = linear_model.LinearRegression()\n",
    "\n",
    "# 使用数据训练模型\n",
    "regr.fit(x, y)\n",
    "\n",
    "# 拟合模型\n",
    "print(\"The linear model is: Y = {:.5} + {:.5}*维度 + {:.5}*海拔\".format(regr.intercept_[0], regr.coef_[0][0], regr.coef_[0][1]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "之后，可以直接调用regr实例的Methods，获取想要的相关数据：\n",
    "   1. get_params()   获取预测（计算模型用的）参数  \n",
    "   2. predict()     获取预测值\n",
    "   3. score()       可决系数R<sup>2<sup>\n",
    "    \n",
    "标准误差可以用sklearn.metrics.mean_squared_error()获取    \n",
    "  \n",
    "\n",
    "__再者:__ 如果需要更多参数可以使用statsmodel库，也一样几行代码完成回归计算。[statsmodel库API](https://www.statsmodels.org/stable/api.html)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>        <td>年降水量p/mm</td>     <th>  R-squared:         </th> <td>   0.827</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.820</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   119.3</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Tue, 12 May 2020</td> <th>  Prob (F-statistic):</th> <td>9.24e-20</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>16:49:37</td>     <th>  Log-Likelihood:    </th> <td> -312.86</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>    53</td>      <th>  AIC:               </th> <td>   631.7</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>    50</td>      <th>  BIC:               </th> <td>   637.6</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     2</td>      <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "    <td></td>       <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>const</th> <td> 3295.1279</td> <td>  205.455</td> <td>   16.038</td> <td> 0.000</td> <td> 2882.460</td> <td> 3707.796</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>纬度y/度</th> <td>  -81.1737</td> <td>    5.386</td> <td>  -15.071</td> <td> 0.000</td> <td>  -91.992</td> <td>  -70.355</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>海拔a/m</th> <td>    0.0362</td> <td>    0.021</td> <td>    1.733</td> <td> 0.089</td> <td>   -0.006</td> <td>    0.078</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td> 1.809</td> <th>  Durbin-Watson:     </th> <td>   1.347</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.405</td> <th>  Jarque-Bera (JB):  </th> <td>   1.677</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 0.330</td> <th>  Prob(JB):          </th> <td>   0.432</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 2.431</td> <th>  Cond. No.          </th> <td>3.03e+04</td>\n",
       "</tr>\n",
       "</table><br/><br/>Warnings:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.<br/>[2] The condition number is large, 3.03e+04. This might indicate that there are<br/>strong multicollinearity or other numerical problems."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:               年降水量p/mm   R-squared:                       0.827\n",
       "Model:                            OLS   Adj. R-squared:                  0.820\n",
       "Method:                 Least Squares   F-statistic:                     119.3\n",
       "Date:                Tue, 12 May 2020   Prob (F-statistic):           9.24e-20\n",
       "Time:                        16:49:37   Log-Likelihood:                -312.86\n",
       "No. Observations:                  53   AIC:                             631.7\n",
       "Df Residuals:                      50   BIC:                             637.6\n",
       "Df Model:                           2                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "const       3295.1279    205.455     16.038      0.000    2882.460    3707.796\n",
       "纬度y/度        -81.1737      5.386    -15.071      0.000     -91.992     -70.355\n",
       "海拔a/m          0.0362      0.021      1.733      0.089      -0.006       0.078\n",
       "==============================================================================\n",
       "Omnibus:                        1.809   Durbin-Watson:                   1.347\n",
       "Prob(Omnibus):                  0.405   Jarque-Bera (JB):                1.677\n",
       "Skew:                           0.330   Prob(JB):                        0.432\n",
       "Kurtosis:                       2.431   Cond. No.                     3.03e+04\n",
       "==============================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "[2] The condition number is large, 3.03e+04. This might indicate that there are\n",
       "strong multicollinearity or other numerical problems.\n",
       "\"\"\""
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import statsmodels.api as sm\n",
    "\n",
    "\n",
    "X2 = sm.add_constant(x)\n",
    "regr1 = sm.OLS(y, X2).fit()\n",
    "# 总结\n",
    "regr1.summary()"
   ]
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